Study Population and Sample Size Determination
The study population defines who can answer the question; sample size determines how many observations are required for adequate precision or power. Both must be specified before recruitment.
Learning objectives
- Differentiate target, accessible and study populations.
- Develop defensible inclusion and exclusion criteria.
- Explain sampling frames, units and participant flow.
- Identify inputs required for common sample-size calculations.
- Adjust for non-response, design effect and finite populations.
Population hierarchy
| Term | Meaning | Example |
|---|---|---|
| Target population | Group to which findings are intended to apply | Adults with hypertension in District X |
| Accessible population | Eligible group reachable through chosen settings | Adults registered at four selected clinics |
| Study population | Individuals meeting criteria during the study period | Eligible clinic attendees from June–August |
| Sample | Selected participants providing data | Calculated and recruited subset |
| Sampling frame | Operational list or source used for selection | Updated hypertension register |
Eligibility criteria
Inclusion criteria identify who qualifies; exclusion criteria remove otherwise eligible people for a justified reason. Criteria should follow the question rather than make recruitment convenient. Excluding severely ill, remote or non-literate people may reduce representativeness and must be justified.
Sample-size principles
Precision studies
Require anticipated prevalence, confidence level and acceptable margin of error.
Comparative studies
Require expected effect, outcome frequency or variability, significance level, power and group ratio.
For a large population proportion, a common starting formula is n = Z²p(1−p)/d², where Z is the confidence coefficient, p the expected proportion and d the absolute precision.
Worked example
Expected prevalence p = 0.30, 95% confidence Z = 1.96 and precision d = 0.05: n = 1.96²×0.30×0.70/0.05² ≈ 323. For 10% anticipated non-response, divide by 0.90: 323/0.90 ≈ 359 participants.
Important adjustments
- Non-response: inflate for anticipated refusal or incomplete data.
- Design effect: inflate when clustered observations provide less independent information.
- Finite population correction: may reduce required sample when sampling a large fraction of a small population.
- Multiple objectives: calculate for major objectives and use the largest defensible requirement.
- Subgroup analysis: ensure enough participants in essential strata.
Sample size is not only a formula
An underpowered study may expose participants without answering the question. An unnecessarily large study wastes resources and may expose more people than needed. Assumptions must be sourced and analysis should match the calculation.
Participant flow
- Number assessed for eligibility.
- Number excluded and reasons.
- Number eligible and approached.
- Number consenting and enrolled.
- Number completing follow-up or analysis.
- Missing data and exclusions from analysis.
Common errors
- Using 50% prevalence without explaining why.
- Adding 10% instead of dividing by the expected response proportion.
- Ignoring clustering or loss to follow-up.
- Calculating for prevalence but analysing group differences.
- Confusing sample size with sampling technique.
- Claiming generalisation beyond the target and sampling frame.
Review questions
- Differentiate target and accessible populations.
- Calculate a proportion sample using p = 0.20 and d = 0.05.
- Why does cluster sampling require a design effect?
- Develop eligibility criteria for a diabetes-adherence study.
References
- WHO. Health Research Methodology.
- UAHEB. Research Proposal and Report Writing Guidelines.
Educational content only; final sample sizes should be reviewed by a qualified supervisor or statistician.
